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# Find height of a projectile

Height of a Projectile. A stone is thrown directly upward from a height of 30ft with an initial velocity of 60ft/sec. The height of the stone t seconds after it has been thrown is given by the function
s(t)=-16t^2+60t+30. Determine the time at which the stone reaches its maximum height and find the maximum height.

### 3 Answers by Expert Tutors

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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Finding the vertex coordinates (h, k) to get the time and the maximum height,
h = -b/(2a) = 60/(2*16) = 15/8, k = f(h) = 345/4

Answer: t = 15/8 sec, and the maximum height is 345/4 ft.
4.9 4.9 (226 lesson ratings) (226)
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Hey Daniel -- here's a physical reasoning approach you may like ...

ave speed from start to peak is 30ft/s ... g of 32ft/s/s takes 1 7/8 sec to slow from
60ft/s to zero at peak ... ht is 30ft plus (ave speed * 1 7/8 sec) ==> 90ft less 30/8 ft

==> 86 1/4 ft after 1 7/8 sec ... Best wishes, sir :)
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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S(t) =  -16 t2 + 60t + 30

This is a parabola :  Maximum( -60/ -32 , s( 15/ 8)

t   = 15/8

S( 15/8) = -16(15/8)2 +60*(15/8) + 30 = 86.25